In geometry, area is the 2-dimensional space or region occupied by a closed figure, while perimeter is the distance around a closed figure i.e. the length of the boundary. For example, the area can be used to calculate the size of the carpet to cover the whole floor of a room. Perimeter can be used to calculate the length of fence required to surround a yard or garden. Two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.

Comparison chart

Area

Perimeter

Definition

The space or region occupied by a closed figure.

The distance around a closed figure.

Measurement

Square unit.(sq) Measures two dimensions e.g. 24 in² or 24 inches squared

Linear unit Measures one dimension Eg 24 in. or 24 inches

Usage

For example to carpet the whole room

For example to put a fence around the garden

Square

s², where s is the length of one side of the square.

4s, where s is the length of one side of the square.

Rectangle

lw, where l and w are the length and width of the rectangle.

2l + 2w, , where l and w are the length and width of the rectangle.

Triangle

Sq. root (s*(s-a)(s-b)(s-c)), where s is half the perimeter, a, b and c are the lengths of the sides. OR ½*ab*sin(C), where a and b are any two sides, and C is the angle between them. OR ½*bh, where b is the base and h is height

a+b+c, where a,b and c are the lengths of the sides of the triangle.

Area represents a two-dimensional region; so the unit for area is "square units". e.g. 24 inches squared or 20 centimeters squared. This is written as 20 cm^{2}.

We use linear units when we measure perimeter. Linear units measure one dimension, length.

Cheat sheet of mathematical formulas to calculate area and perimeter for a variety of geometric shapes, including circle, square, triangle, rectangle, equilateral polygons, regular polygons and general polygons.

An irregular shape has sides of different length. Calculating area on these shapes involves breaking the shape down into common shapes like squares, rectangles, triangles and circles. This is because these shapes all have set formulas for calculating their area. Being able to see the shapes within shapes is the key to calculating the area of irregular shapes. After finding the area of each shape add them to get the total area. In the case of perimeter of irregular object just measure the length of each side and add them up.

This is good maybe a few more examples would be better.

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November 23, 2012, 1:20pm

good discussion for mensuration of plane figures....need additional help...can I ask for a very little discussion on spherical mensuration...by spherical, I am referring to limiting it with plane figures in a spherical surface....thanks for your help..will appreciate it...

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